Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-6y &= 5 \\ -2x+6y &= 6\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = 2x+6$ Divide both sides by $6$ to isolate $y$ $y = {\dfrac{1}{3}x + 1}$ Substitute this expression for $y$ in the first equation. $4x-6({\dfrac{1}{3}x + 1}) = 5$ $4x - 2x - 6 = 5$ Simplify by combining terms, then solve for $x$ $2x - 6 = 5$ $2x = 11$ $x = \dfrac{11}{2}$ Substitute $\dfrac{11}{2}$ for $x$ back into the top equation. $4( \dfrac{11}{2})-6y = 5$ $22-6y = 5$ $-6y = -17$ $y = \dfrac{17}{6}$ The solution is $\enspace x = \dfrac{11}{2}, \enspace y = \dfrac{17}{6}$.